I first tried entering my ISP's DNS server number directly into Network manager on both machines. That pretty well took care of the speed problem. It also removed the spurious IP #s ; now I can take those extra entries out from my hosts file. Dig now shows this on both machines:

Nelz, I tried the OpenDNS number (208.67.222.222) but it wasn't as fast as my ISP.

Putting my ISP's DNS server number directly into the Network Managers has "solved" the speed problem at least temporarily. I also tried putting the numbers into my router and pointing Network Manager at the router, but that's slow again. My friend dropped off the loaner modem but I wasn't able to get it going, so he will be back. It's better to have everything in the router and the modem.

That sounds like what my friend said, only he thinks it's the modem. We just hadn't realized the fix for that problem would also fix the problem with those spurious IP numbers in dig. I'll mention your suggestion to him and post back when I know something.

In faith, Dave
Viva Texas

By golly, I'm beginning to think Linux really *is* the best thing since sliced bread.

I figured out how to get the loaner modem working (I had to get its ip# from the router - 10.0.0.1); but it worked right off the bat and it looks like my speed is completely restored. Also, the 'Dig' output looks better (I think):

At least the dig output is simpler now. My friend won't be able to get back until Monday or maybe Tuesday, but I'll post what he finds out. He wants to do a firmware update on the router, but he wanted to wait until the speed problem was solved.

Dig is failing - "ANSWER: 0" - because your ISP's DNS server doesn't know about your local addresses. That's why you should have the ISP's DNS server in the modem or router and let the router answer all your queries.

"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)

I think you're digging in to deep (s'cuse the pun ). Have your friend update the firmware using the fixed DNS first, then try working with the DHCP server in the router again. It'll be a PITA on your normal network use, but at least your internet is working.

PS: DNS changes need time to propagate. How much depends on the TTL: time to live. It's a value for how long a specific set of data can be trusted to be up-to-date and when that time (from a marked time) has passed, the recipient needs to request another, valid data packet. A common value is 1,500 (measured in seconds), or 25 minutes. So if the recipient has received a valid data set at 16.43h, it'll request a new set at 17.08h, but in the interim, it'll consider the 16.43h data set valid and correspond accordingly.